def draw_ellipse(position, covariance, ax=None, **kwargs):
"""Draw an ellipse with a given position and covariance
Inspired By: VanderPlas, Jake (2016). Python Data Science Handbook. O'Reilly Media, Inc. ISBN: 9781491912058
"""
# Convert covariance to principal axes
if covariance.shape == (2, 2):
U, s, Vt = np.linalg.svd(covariance)
angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))
width, height = 2 * np.sqrt(s)
else:
angle = 0
U, s, Vt = np.linalg.svd(covariance)
width, height = 2 * np.sqrt(s[:2])
# Draw the Ellipse
for nsig in range(1, 4):
ax.add_patch(Ellipse(position[0], nsig * width, nsig * height, angle, **kwargs))
def plot_gmm(
gmm_metrics_df: pd.DataFrame,
gmm_labels_df: pd.DataFrame,
pca_model: PCA,
k: int,
ax=None,
):
"""Plot the GMM clusters with varying levels of certainty.
Inspired By: VanderPlas, Jake (2016). Python Data Science Handbook. O'Reilly Media, Inc. ISBN: 9781491912058
Args:
gmm_labels_df (pd.DataFrame): DataFrame containing gmm labels and PCA datapoints for each model
gmm_metrics_df (pd.DataFrame): DataFrame containing properties of each model.
pca_model (PCA): PCA model already fitted on the data
k (int): Number of clusters to draw
ax (_type_, optional): Axis on which to draw the figure. Defaults to None.
reverse (bool, optional): Reverse the palette colors. Defaults to False.
"""
# Get palette
unique = gmm_labels_df[f"{k}_clusters_labels"].unique()
palette = dict(zip(unique, sns.color_palette(n_colors=len(unique))))
palette = list(map(lambda x: x[1], sorted(palette.items())))
sns.scatterplot(
gmm_labels_df,
x="PCA1",
y="PCA2",
hue=f"{k}_clusters_labels",
palette=palette,
ax=ax,
)
# Get metrics
weights = gmm_metrics_df.loc[gmm_metrics_df["n_clusters"] == k, "Weights"].values[0]
means = gmm_metrics_df.loc[gmm_metrics_df["n_clusters"] == k, "Means"].values[0]
covariances = gmm_metrics_df.loc[gmm_metrics_df["n_clusters"] == k, "Covariances"].values[0]
# Draw ellipse
w_factor = 0.15 / weights.max()
for pos, covar, w, c in zip(means, covariances, weights, palette):
draw_ellipse(
position=pca_model.transform(pos.reshape(-1, 7)), # Transform the cluster centers using previously fitted PCA model
covariance=covar,
alpha=w * w_factor,
ax=ax,
color=c,
)
# Set title
ax.set_title(f"{k} Clusters")
fig, axes = plt.subplots(3, 3, figsize=(15, 15), sharex=True, sharey=True)
axes = axes.flatten()
for i, ax in enumerate(axes):
plot_gmm(gmm_metrics_df, gmm_labels_df, seeds_pca, i + 2, ax=ax)
ax.get_legend().remove()
plt.suptitle("GMM Clustering");
